Adaptive Edge Analytics for Distributed Networked Control of Water Systems
Sokratis Kartakis, Weiren Yu, Reza Akhavan, and Julie A. McCann
Department of Computing, Imperial College London, UK
{s.kartakis13, weiren.yu, reza.akhavan, j.mccann}@imperial.ac.uk
Abstract—Over the last decade, there has been a trend
where water utility companies aim to make water distribution
networks more intelligent in order to improve their quality of
service, reduce water waste, minimize maintenance costs etc.,
by incorporating IoT technologies. Current state of the art
solutions use expensive power hungry deployments to monitor
and transmit water network states periodically in order to
detect anomalous behaviors such as water leakage and bursts.
However, more than 97% of water network assets are remote
away from power and are often in geographically remote
underpopulated areas; facts that make current approaches
unsuitable for next generation more dynamic adaptive water
networks.
Battery-driven wireless sensor/actuator based solutions are
theoretically the perfect choice to support next generation
water distribution. In this paper, we present an end-to-end
water leak localization system, which exploits edge processing
and enables the use of battery-driven sensor nodes. Our system
combines a lightweight edge anomaly detection algorithm based
on compression rates and an efficient localization algorithm
based on graph theory. The edge anomaly detection and
localization elements of the systems produce a timely and
accurate localization result and reduce the communication
by 99% compared to the traditional periodic communication.
We evaluated our schemes by deploying non-intrusive sensors
measuring vibrational data on a lab-based water test rig that
have had controlled leakage and burst scenarios implemented.
Keywords-IoT, Cyber-Physical Systems, Wireless Sensor Networks, Anomaly Detection, Burst Localization
I. WATER D ISTRIBUTION
AND
S ENSOR N ETWORKS
Water security is currently a hot topic. Water demands
are not being met in regions of the world; both developed
and underdeveloped; where climate change and economic
water scarcity are two issues that have the largest impact.
The former sees areas of the planet less able to generate
enough water for its people, whereas in economic scarcity
the principality is unable to build or maintain a water
distribution network to continuously meet demands. Drought
prone areas such as California in the USA have had severe
water restrictions in place for some time. Wet countries, such
as the UK, have been experiencing what has been termed
wettest droughts over the past few years. Notwithstanding
the 7.5bn investment in UK water distribution networks,
3.3bn litres of water were lost per day in 2010 [1].
The use of sensing systems to identify water leakage
have been around for some time [2], but their uptake has
not been prolific. ICT to support WDN typically consists
of remote or online battery-powered telemetry units (data
loggers) that record water data such as flow and pressure,
over numbers of minutes, then aggregate this data and send
to a server periodically - typically via the mobile phone
networks. Contemporary approaches use Wireless Sensor
Network (WSN) [2], [3], [4], [5], [6] technologies to monitor
the status of the water network and detect leakage or water
bursts closer to real-time. The main drawbacks of these
approaches are: (a) the analysis of the data takes place offline, in base-stations or servers meaning that optimal real
time decision-making for control would be unrealistic and
(b) the sensor nodes require a lot of energy, which places
upper bounds on the amounts of data that can be sensed and
relayed for analysis. The latter issue particularly impacts on
what is important to water companies, leakage localization.
Given the cost of digging up roads to fix leaks, timely and
accurate determination of the location of a leak is now
more important than identifying all leakages. However, to
carry out localization high-fidelity sensing and analytics are
required to triangulate leakage accurately; current systems
are not quite there yet.
In parallel, civil engineers advocate that next generation
water networks will not be passive water delivers, but
active highly-distributed control systems that route the water
intelligently to match demand and route round failures etc.
[7]. Such a dynamical system will heavily rely on sensing
and actuation and will effect a dual control system of a
water distribution network coupled with a smart distributed
sensor/actuator network. This will require that both networks
interact in a complex cyber-physical way and make use
of state-of-the-art low-powered high-precision sensing and
processing technologies. It is our premise that state of the
art high-precision sensors can help build such a system, but
that it is too costly, and not very useful, to send all this
higher precision data back to off-line servers for processing.
That is, much of the identification of a leak can be carried
out on edge devices (i.e. the sensor nodes) and they can
collaborate to localize that leak and carry out control. This
is a step change from the tradition of sending periodic data
to servers to make control decisions, replacing it with a
distributed event-based control system.
This paper presents a highly distributed lightweight
scheme that combines compression and anomaly detection to
identify and locate water leak events and is the first steps to
the aforementioned distributed event-based control system.
On event detection we only need to send timestamp data
II. E DGE -A NALYTICS
Figure 1: System architecture: sensor nodes,communication,
and server side system.
to our novel graph topology-based scheme that recursively
examines data from pairs of sensor nodes that detect an
anomaly simultaneously to localize the leak. Though inspired by water distribution network leakage management,
these algorithms are designed for generic sensing and analytics for other pipe based cyber-physical systems and beyond.
Here we focus on the event detection and localization, the
complete control function is outside the scope of this paper.
The work presented here has been developed as part of our
smart water projects at Imperial where we show that we can
not only significantly reduce the amount of communications
between sensor devices and servers, but also that early
transient or event (such as water bursts) detection can run
on low-resourced sensor nodes meaning that local control
functions can occur with minimal latency. The event detection software uniquely uses compression rates rather than
raw data for analysis. The localization scheme demonstrates
that it substantially improves positioning accuracy through
capturing the water network topology information without
sacrificing computational efficiency. The search algorithm
combines average distances in the abstractions of the water
network topology with differences in arrival times of the
sensed anomaly as detected at the sensor locations. As far
as we are aware we are the first to provide an edge analytics
solution to water network distribution systems and the first
to combine this with highly efficient graph processing to
localize leaks.
This paper is organized as follows: Sections 2 and 3
presents the edge anomaly detection algorithm and the selftuning system based on active learning. Section 4 proposes
efficient graph-based techniques to effectively localize water
burst events. Section 5 demonstrates the experimental environment followed by the empirical evaluation in Section 6.
Section 7 surveys the related work and Section 8 concludes
the paper.
FOR
A NOMALY
DETECTION
To provide a non-intrusive solution to leakage localization
we fit sensor nodes to water pipes. For this project we use
the NEC Tokin Ultrahigh-Sensitivity Vibration Sensor that
covers a frequency band of 10 to 15 kHz (and acceleration at
0.0001 G) with very low power requirements [8]. Such high
fidelity sensors allow us to better explore water network transient phenomena, but the cost of fully transmitting that data
is prohibitive using battery powered low-resourced devices.
Therefore, each sensor node utilizes lossless compression
techniques which reduce the energy cost related to the
communication without sacrificing the precision of the data.
After extensive evaluation of different lossless compression
algorithms [9], miniLZO [10] was selected as the most
appropriate algorithm. Our choice takes typical MCU class
devices memory and energy constraints into account, e.g.
typical ultra-low power MCUs have 64Kbytes memory [11],
therefore we limit the compression algorithms working space
to 10K.
We now introduce our anomaly detection algorithm that
uniquely does not analyse raw data for anomalies that
could be leaks, but instead automatically detects significant
changes in compression rates in the compressed data and
in doing so identifies the timestamps of anomalies that
represent leaks [9]. In this paper, we use vibration data vibration sensors fixed externally to the pipe providing a
less intrusive and lower cost sensing solution attractive to
water companies. Initially, the input stream is separated into
windows of wstream bytes (i.e. 512 bytes) and for each
window, the sensor node applies lossless compression and
produces a compression rate value. Figure 2a illustrates both
raw pressure data and compression rate (noisy signal). To
maximize anomaly detection while minimizing the number
of false-positive results, noise is removed from the compression rate stream using a one-dimensional Kalman Filter [12],
[13] indicated in Figure 2 and Figure 3 with a blue line.
The use of Kalman filters is motivated by: (a) their support
for streaming analysis using only current input measurements (therefore making the solution more memory efficient), (b) they do not require matrix calculations (therefore
the solution is more computationally efficient), (c) the ease
of the algorithm tuning process, and (d) their implementation
simplicity. During the initialization process the parameters
which need tuning are the process noise covariance q, the
sensor measurement noise covariance r, the initial estimated
error covariance p and an initial measurement x (i.e. q =
0.005, r = 25, p = 0, and x = the first compression rate
measurement). Afterwards, for every new compression rate,
the Kalman filter algorithm updates these parameters and
produces the filtered value of compression rates. After noise
removal, the anomalies can be detected accurately as can
be seen in Figure 2a the anomalies are presented as great
drops (arrows). The anomalies are being detected by using
(a) Raw data, compression rates, and Kalman filter results.
Figure 3: Anomaly detection over vibration data from NEC
Token sensors externally fixed to the water pipe
(b) Anomaly detection results
Figure 2: Anomaly detection based on water pressure data.
an adaptive thresholding approach based on the mean and the
standard deviation of the compression rate moving average
for a predefined window size wmavg (i.e. 128). We use this
because it smooths states for easier analysis and reduces
threshold computations to window sizes. Specifically, the
algorithm computes the moving average of the filtered
compression rates (x values), with the average avg and
the standard deviation std of the moving average. In every
Kalman state update, the algorithm identifies as an anomaly
the values which hold the following condition:
x > (avg + std ∗ l) or x < (avg − std ∗ l)
where l represents the elasticity of anomaly detection
(smaller values mean that the system is more sensitive Figure 4).
As can be observed in Figure 4a, the algorithm suffers
from a cold start effect (it identifies the first values to be
outliers because the moving average is yet to be calculated).
To solve this problem, the algorithm initializes the avg
and computes std by using the current compression rate
value. Another challenge occurs where there is a significant
variation of compression rate data detected (Figure 4a). In
that case, because the standard deviation has a high value,
this indicates that the algorithm requires more intervals for
the moving average calculations to detect the outliers or
anomalies. The solution is to reset the values, that is, to
initialize the avg and std, every time the distance between
the thresholds created by the standard deviation become
greater than a specific value t (in our system the t = 35).
Figure 4b illustrates the anomaly detection results after the
reset feature application.
Based on the above analysis, by tuning the input parameters, our algorithm can be applied to any case of high
sample rate anomaly detection (i.e. pressure, vibration - see
Figure 3) in hardware constrained sensor nodes. However,
to maximise the performance of the algorithm, a self-tuning
technique is required thus bringing Autonomic properties to
the system.
By exploiting this edge anomaly detection algorithm,
communication costs can be reduced significantly. The localization system requires only the anomaly detection arrival
times from every sensor node. Therefore, each sensor transmits timestamps only instead of raw data, and only whenever
an anomaly is observed at the edge. This is in contrast to the
traditional periodic sense and send routine of current water
network sensing solutions as well as many WSN systems
in general. It also better fits modern distributed event-based
control systems such as [14].
Table I: Algorithm parameters
Process
Input stream split windows size
Kalman Filter initialization
Moving average window size
Threshold Elasticity
Reset Threshold
Parameters
wstream
Process noise covariance q
Sensor measurement noise covariance r
Initial estimated error covariance p
wmavg
l
t
(a)
Figure 5: Anomaly detection parameter tuning.
label anomalies on a subset of our evaluation data. Then,
we created an offline cross-evaluation system [9], which
uses our algorithm and calculates the correct, false/positive
(F P ), and true/negative (T N ) anomaly detections based
on the initial labelling. This establishes the optimal input
parameters as the combination that maximizes the distance:
Distance D = [Correct − (F P + T N )] Detections
(b)
Figure 4: Filtered compression rates and anomaly detection
based on (a) pressure data and (b) vibration data(a) Cold
Start, Large Variation and inelastic outliers detection (l =
1.5), and (b) fixed algorithm results (l=3).
III. O PTIMAL S ELF -T UNING VIA ACTIVE L EARNING
By tuning the input parameters, our algorithm can be
applied to any case of high sample rate anomaly detection in
hardware constrained sensor nodes. Table 1 lists the tuning
parameters required by our edge algorithm. In order to
optimize the tuning process of the algorithms, we borrow
ideas from active learning techniques [15]. Here true anomalies for a single representative training dataset are labelled.
For the results that we present here, we applied the active
learning idea by asking water data technicians to manually
Using this, one can imagine that a system would update
parameters to re-update the in-node anomaly detection algorithm as the water network evolves. We not only use
anomaly identification but also leakage localization in the
labelling process; this extends our prior work significantly.
IV. WATER B URST E VENT L OCALIZATION
In this section, efficient graph-based techniques are used
to efficiently and accurately localize the water burst event.
We first devise a novel graph topology-based measure that
can quantify the “average length” between every two senor
locations, and then define our search method to localize burst
events.
A. Graph Topology-Based Measures
A water network can be modelled as an attributed graph
G = (VJ ∪ VS , E, A), where VJ is a vertex set of pipe
junctions, VS is a vertex set of deployed sensor locations, E
denotes an edge set of pipe sections connecting two vertices,
and A carries the length of each pipe section.
c
a
f
b
a
8
g
e
b
6
d
j
i
2
f
7
g
d
2
5
4
e
h
c
3
h
6
3
j
4
i
Figure 6: Modelling a water network (left) as a weighted graph (right) based on graph topology
To evaluate the “average length” between every two
vertices in a graph G, let us first introduce the notions of
the distance matrix D and the adjacency matrix A.
Definition 1: Given a water network G = (VJ ∪VS , E, A)
with |V | = |VJ | + |VS | vertices and |E| edges, its distance
matrix D is a |V | × |V | matrix, with its entry Du,v being
the length of pipe section (u, v), if (u, v) ∈ E;
Du,v =
0,
otherwise.
The adjacency matrix of G, denoted as A, is defined by
1, if u 6= v and ∃ pipe section (u, v) ∈ E;
Au,v =
0, otherwise.
Example 1: Figure 6 depicts the water network G, whose
edge weights are the length of pipe sections. By Definition 1,
its distance matrix D and adjacency matrix A are
a
b
c
d
D=
e
f
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A=
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Utilizing D and A, we can determine the “average length”
between every two sensor locations on graph G.
We first introduce a |V | × |V | matrix, W(d) , whose entry
[W(d) ](u,v) is the “average length” of all paths with d hops
between vertices u and v, that is,
[W(d) ](u,v) =
the sum of the pipe section lengths over all paths with d hops between vertices u and v
.
the number of the paths with d hops between vertices u and v
(1)
To obtain the denominator of Equation (1), we can utilize
the property of the power of an adjacency matrix. That is, the
(u, v)-th element of the d-th power of A, that is, [Ad ](u,v) ,
counts the number of the paths with d hops between vertices
u and v.
However, evaluation of the nominator of Equation (1)
is non-trivial as the power of a distance matrix can only
evaluate the product (instead of sum) of the pipe section
lengths over all paths. As an example in Figure 6, to
determine the sum of the pipe section lengths over all paths
with 2 hops between vertices d and g, the result of [D2 ](d,g)
would produce the product of the pipe section lengths as
follows:
[D2 ](d,g)
= (the d-th row of D) × (the g-th column of D)
=
a
b
8
6 0
c
d
e
f
g
h
i
0 2
0 0
4 0
c
e
g
a
b
0
7 0
d
0 0
f
0 0
h
j
0 ·
i
j
5 0
0
= 6×7 + 5×4 6= (6+7) + (5+4)
| {z } | {z }
d→b→g
T
(2)
d→h→g
We notice that, if the “×” sign in Equation (2) were
changed into “+” sign, the result would turn into the more
desirabe sum of the pipe section lengths over all paths
(d → b → g and d → h → g) with 2 hops between vertices
d and g. To obtain the correct “+”-based results, we can
perhaps take advantage of the power of a distance matrix
while changing its “×” sign (in Equation (2)) into “+” sign
as well?
To address this, we introduce an element-wise operator
exp(∗). We construct the element-wise exponential distance
matrix, denoted as exp(tD), as follows:
exp (tDu,v ), if Du,v 6= 0;
[exp(tD)]u,v =
0,
if Du,v = 0.
where t ∈ R denotes an arbitrary scalar.
Intuitively, the matrix exp(tD) is formed by replacing
every nonzero element in D, say x, with ex , and keeping
the zero elements of D unchanged.
Then, to assess the sum of the pipe section lengths over
all paths with 2 hops between vertices d and g, we compute
the (d, g)-th element of (exp(tD))2 , that is,
[(exp(tD))2 ](d,g)
=
=
(the d-th row of exp(tD)) × (the g-th column of exp(tD))
a8t b6t c d e2t f g h4t i j e
e
0 0 e
0 0 e
0 0 ·
a
=
6t
b
7t
c
0 e
0
7t
5t
d
e
0 0
e ×e + e ×e
4t
f
g
0 0
=e
h
5t
e
(6+7)t
i
T
(5+4)t
(3)
In contrast to Equation (2), we can see that, by utilizing
the operator exp(∗), Equation (3) converts all “×” signs into
“+” signs. In light of Equation (3), our next step is to find
out an “inverse” operator that can map e(6+7)t +e(5+4)t back
into (6 + 7) + (5 + 4). Our key observation is that
2
1 xt
yt
lim log
=x+y
(4)
e +e
t→0 t
2
Thus, applying the “inverse” operator lim 2t log 21 (∗) of
t→0
Equation (4) into Equation (3) produces
1
2
[(exp(tD))2 ](d,g)
lim log
t→0 t
2
2
1
= lim t log 2 e(6+7)t + e(5+4)t
t→0
=
(6 + 7) + (5 + 4)
(6+4+4)t
(7+5+4)t
[(exp(tD))3 ](b,i) = |e(6+2+6)t
{z } + e| {z } + e| {z }
b→d→e→i
j
0 0
+e
for arbitrary element (u, v) of (exp(tD))k in Equation (3)
should be consistent with (i) the choice of N in Equation (6)
and (ii) the number of paths with d hops between vertices
u and v (that is, [Ad ](u,v) ).
Example 2: Consider the water network in Figure 6. To
compute the sum of the pipe section lengths over all paths
with d = 3 hops between vertices b and i, we first obtain its
distance matrix D and adjacency matrix A (see Example 1).
Next, we evaluate [A3 ](b,i) = 3 and
(5)
whose result gives the sum of the pipe section lengths over
all paths (d → b → g and d → h → g) with 2 hops between
vertices d and g.
Equations (3)–(5) provide an effective technique to obtain
the nominator of [W(d) ](u,v) in Equation (1). To generalize
our above result for any arbitrary element of (exp(tD))2 ,
we need to extend the “inverse” operator in Equation (4):
Theorem 1: For any positive integer N = 1, 2, · · · , the
following equation holds:
1 x1 t
N
x2 t
xN t
e + e + ··· + e
log
lim
t→0 t
N
= x1 + x2 + · · · + xN . (6)
As a special case of N = 2, Theorem 1 reduces to the
result in Equation (4). Theorem 1 is used for generalizing the result of Equation (3) for any arbitrary element
of (exp(tD))k . More specifically, in our aforementioned
example, we choose Equation (4) (that is, N = 2 in
Equation (6)) to “inverse” [(exp(tD))2 ](d,g) because there
are two summands (e(6+7)t and e(5+4)t ) in Equation (3). In
the general case, we observe that the number of summands
b→d→h→i
b→g→h→i
Finally, choosing N = 3 in Theorem 1, we can “inverse”
[(exp(tD))3 ](b,i) as follows:
3
1
lim log
[(exp(tD))3 ](b,i)
t→0 t
3
(6+2+6)t
e
+ e(6+4+4)t + e(7+5+4)t
3
= lim log
t→0 t
3
= (6 + 2 + 6) + (6 + 4 + 4) + (7 + 5 + 4) = 44.
Hence, the sum of the pipe section lengths over all paths
with 3 hops between vertices b and i is 44.
After the nominator of Equation (1) is obtained, the
“average length” [W(d) ](u,v) follows immediately:
Theorem 2: The “average length” of all paths with d hops
between every two vertices u and v can be computed as

[(exp(tD))d ](u,v)

1
, if [Ad ](u,v) 6= 0;
lim log
[Ad ](u,v)
t→0 t
[W(d) ](u,v) =
 0,
if [Ad ]
= 0;
(u,v)
As a special case, W(1) = D. This is because, when
d = 1 and u 6= v, [Ad ](u,v) = 1. Then,
[W(1) ](u,v) = lim
t→0
log([exp(tD)](u,v) )
t
= lim
t→0
[(tD)](u,v)
t
= D(u,v) .
Example 3: Recall Example 2. Since [A3 ](b,i) = 3 and
the sum of the pipe section lengths over all paths with d = 3
hops between vertices b and i is 44, the “average distance”
is
[W(3) ](b,i) = 44/3.
Theorem 2 gives an effective way to evaluate the “average
length” [W(d) ](u,v) with a fixed number d of hops in terms
of D and A. Based on [W(d) ](u,v) , we can obtain the
“average length” matrix S(L) within L hops as follows.
Definition 2: Let 0 < λ < 1 be a user-controlled decay
factor. Given a water network G, its “average distance”
matrix S(L) within L hops (L = 2, 3, · · · ) is defined by
(L)
[S
](u,v) =
(
1
β
h
i
λD + λ2 W(2) + · · · + λL W(L)
0,
(u,v)
,
(u 6= v);
(u = v).
(7)
where
β=
L
X
at locations u and v). We observe that the time gap between
(tu − tx ) and (tv − tx ) (which can be calculated as |tu − tv |)
is mainly due to the difference in “average length” from the
burst (source) location x to both sensor locations u and v.
Hence, ideally we have the following equations:
i
λ · 1{[W(i) ](u,v) 6=0} .
i=1
Here, 1{[W(i) ](u,v) 6=0} is an indicator function, which returns
1 if [W(i) ](u,v) 6= 0, and 0 otherwise.
Intuitively, [S(L) ]u,v captures the weighted average distance within L hops between vertices u and v. In Equation (7), the first term λD signifies that the paths of 1 hop
have a contribution of λ to S(L) ; the second term λ2 W(2)
means that the paths of (longer) 2 hops have a (smaller)
contribution of λ2 to S(L) , and so forth. The parameter β1
is a normalization factor, which guarantees that the sum of
all the weighted factors {λ, λ2 , · · · , λL } in Equation (7) is
1.
The constant λ is between 0 and 1, which can be thought
of as a confidence level. Empirically, it is set to 0.6–0.8,
representing the rate of decay as the leak signature wave
spreads across pipe sections.
Example 4: Recall the water network in Figure 6 and its
distance matrix D and adjacency matrix A in Example 1. We
choose λ = 0.85 and L = 5. By Definition 2, the “average
length” matrix S(5) can be obtained as follows: S(5) =
a
b
c
d
e
f
g
h
i
j
















tu − tv = (tu − tx ) − (tv − tx ) ⇒
dist(u,x)
which implies that
≈ [S(L) ]u,x − [S(L) ]v,x
X̂ = arg (top-k) min{|ν̄(tu − tv ) − ([S(L) ]u,x − [S(L) ]v,x )|} (9)
x∈V
b
c
d
e
f
g
h
i
j
17.902
0
9.667
12.999
12.214
8.512
13.998
14.512
18.424
17.512
20.609
9.667
0
12.609
14.973
6.159
13.512
17.306
17.666
17.000
14.996
12.999
12.609
0
9.395
14.609
14.707
10.792
11.902
10.729
14.162
12.214
14.973
9.395
0
13.000
17.465
11.434
11.271
14.434
19.000
8.512
6.159
14.609
13.000
0
15.512
16.000
19.666
19.000
22.707
13.998
13.512
14.707
17.465
15.512
0
11.853
12.902
11.772
15.729
14.512
17.306
10.792
11.434
16.000
11.853
0
10.273
8.951
19.902
18.424
17.666
11.902
11.271
19.666
12.902
10.273
0
10.382
18.729
17.512
17.000
10.729
14.434
19.000
11.772
8.951
10.382
0
Having evaluated the “average length” matrix S(L) , we
next present an efficient algorithm to position a water loss
event with higher accuracy.
Our basic idea is to measure the difference in “average
length” to two sensor locations that detect the burst transient
at given times. Specifically, let ν̄ denote the average wave
speed, and let tu and tv be the time points when the burst
transient event is detected at sensor locations u and v,
respectively. Note that the sensor points in the water network
are time synchronized, and the time of the burst event tx
is unknown in advance, but such a burst event must occur
before min{tu , tv } (earlier than either of the detected time
(8)
Then, we can enumerate each sensor location in V to find
out the top-k (k is often set to 3–5 in practice) that best
approximate solutions X̂ ⊆ V of x to Equation (8), that is,
a
B. Effectively Localizing Water Loss Events
dist(v,x)
ν̄(tu − tv ) = dist(u, x) − dist(v, x)
0
17.902
20.609
14.996
14.162
19.000
22.707
15.729
19.902
18.729
As opposed to the previous work [16] that considers only
one single path of the shortest length, S(L) can capture
multiple paths of different lengths between every two sensor locations by fully exploiting water network topology
information. Thus, if the “average length” S(L) is used to
quantify the wave distance travelled from a burst location to
a sensor location, water loss events can be positioned more
accurately, as will be shown in the next section.
ν̄(tu − tv ) = ν̄(tu − tx ) − ν̄(tv − tx )
| {z } | {z }
Thus, the elements in X̂ form a “hyperbolic curve” with two
focal points u and v. To determine the precise location along
this “hyperbolic curve”, we need to choose another pair of
sensor locations, say u and w, as two focal points, with the

aim to produce the another “hyperbolic curve”, that is, to


find out another set of the top-k best approximate solutions


Ŷ ⊆ V to the following equation:






Ŷ = arg (top-k) min{|ν̄(tu −tw )−([S(L) ]u,y −[S(L) ]w,y )|} (10)
y∈V
The intersection of the two “hyperbolic curves” X̂ ∩ Ŷ will
produce a small number of possible locations where a water
loss event may occur. Finally, we can search locally for the
most likely water loss position along pipe sections connected
to the closest sensor locations in X̂ ∩ Ŷ .
V. E XPERIMENTAL S ETUP
The ultimate aim of this Smart Water project is to study
and develop real-time control algorithms that take feedback
from sensors and aim to respond to anomalies, demand
changes, and reconfiguration in an optimal fashion. In this
project we used a lab-based test rig (Figure 7) which
was instrumented with sensor nodes based on Intel Edison
development boards and NEC Tokin Ultra high-sensitivity
vibration sensors.
Figure 7 illustrates the infrastructure of the water network
test rig which is housed in a 10x7m room. On top of this
infrastructure, 7 nodes equipped with vibration sensors were
deployed to the right area of the rig. Figure 7 presents
only three nodes which produce non redundant data and are
located in 2m, 8.7m, and 13.7m distances from the burst
location respectively.
Figure 7: Lab-based pipe rig floor plan and infrastructure.
(a)
(b)
(c)
Figure 8: Anomaly detection from three sensor nodes (A, B, and C) which are located 2m, 8.7m, and 13.7m from the burst
respectively.
VI. E VALUATION
Using the aforementioned infrastructure, a variety of burst
emulations were conducted with different pressure levels and
observed using vibration data (1000 samples per second)
from 7 sensor nodes. For sake of brevity, the non-redundant
data from the three sensor nodes of Figure 8 were used. Figures 9 illustrate the results of the in-node anomaly detection
algorithm that resides in nodes (A, B, and C) and using
16000 data points. For this we represent the water burst on
a highly pressurised water network. Table II aggregates the
performance of the in-node decision-making algorithm based
on average compression, anomaly detection accuracy, and
communication savings for transmitting compressed data or
only timestamps.
A. Compression Rates
Data fluctuation influences the performance of the compression algorithm and the position of the node in the
topology means that data fluctuation rates differ. In this case
the closest node to the burst (Node A) performs the lowest
average compression rate. However even with this high level
of fluctuation, the compression algorithm achieves more than
28% average compression rate.
B. Anomaly Detection
The accuracy of the algorithm for all the nodes is greater
than 90% for the dataset. The remaining 10% error is due
to specificity as the current version of the algorithm remains
slightly conservative. For subsequent work we would adjust
the processing to filter this data and identify outliers.
Table II: Edge Processing Evaluation Results
Node A
Node B
Node C
Average
Compression Rate
Observed
Anomalies
Real
Anomalies
Anomaly Detection Accuracy
Communication
Savings
(Transmit Compressed Data)
28.01%
30.06%
39.25%
18
11
8
20
12
8
90%
91%
100%
79.26%
87.69%
92.22%
C. Communication Savings
Table II presents two different communication types. In
the first type, the node transmits the compressed data only
when an anomaly is locally observed with a result that
reduces communication by 79.26%; this is for the worst case
of (Node A) compared to the base-line scenario of periodic
transmission which is how such data is relayed today. On
the other hand, the second communication type is where we
only send timestamps to the localization algorithm which
saves more than 99% communication.
Communication
Savings (Transmit
Timestamps)
99.88%
99.93%
99.95%
only
radius is 0.5m because any burst event that occurs along the
pipe section ab (whose length is 0.5m) will produce the same
time difference information. More precisely, as depicted in
Figure 10, let x and y be the locations of any two burst
events occurring along the pipe section ab. Then, the time
differences from any burst location to both A and B are
exactly the same. That is,
=
|t(⋆→A) − t(⋆→B) | = |t(b→A) − t(b→B) |
|(t(x→b) + t(b→A) ) − (t(x→b) + t(b→B) )|
=
|(t(y→b) + t(b→A) ) − (t(y→b) + t(b→B) )|
D. Burst Event Localization
This tells us that, by using the time difference information,
the burst event can be determined inside a circle whose
center point at node ⋆ with guaranteed ±0.5m accuracy.
a
B
x
y
A
0.5m
b
Figure 10: ±0.5m accuracy in localizing the burst event
VII. P RIOR R ELATED W ORK
Figure 9: Anomaly detection periods.
To estimate the burst location, we use the proposed
methods as per Equations (9) and (10) to localize the water
burst event. The sound velocity in PVC is 2395 m/sec. By
using the time stamp information from all sensor locations
in Figure 8, we can compute the difference in arrival times
for every pair of sensor locations. Figure 9 illustrates the
anomaly periods from the three individual nodes, as defined
in server side, and allows easier interpretation of anomaly
arrival time differences. First, we use the time difference
between node A and B, which will produce a “hyperbolic
curve” with A and B being two focal points. Next, we use
the time difference between node A and C, which will yield
another “hyperbolic curve” with A and C being two focal
points. The two “hyperbolic curves” will intersect at node ⋆
within an error radius no more than 0.5m. Note that the error
In the realm of Civil Engineering, there have been numerous mechanisms used to detect leaks using novel devices that
mostly focus on intrusive sensing techniques such as in-pipe
sensors or even mobile sensor bots that roam within the pipe
network. Some of this prior work we touch on below, but a
comprehensive review is too voluminous for this publication.
Our work is instead focused on less intrusive approaches
that can specifically form a cost-effective distributed control
system to implement the next generation dynamic water
network topology. The work related to this briefly discussed
in this section.
Edge processing. In current smart water networks, physical
states such as water pressure or pipe vibration are sampled
at a reasonably high frequency (e.g. more than 128 samples
per second) and stored in underground battery-driven sensor
nodes. Currently, such raw data transmission is via cellular
networks which is very costly. The alternative is to transmit
over long-range (several kilometers) wireless communications, however high transmission power is required that leads
to fast battery depletion. Current state of the art solutions
[6] are unable to support underground battery driven sensor
nodes and therefore the typical choice remains to be the
expensive over ground sensor nodes directly connected to
power and transmit data periodically every 15minutes using
3G.
Furthermore, these solutions use offline computationally
intensive algorithms to detect anomalies and require large
amounts of historical data, leading to the inability of the
algorirthm to be distributed and deployable on sensor nodes.
For example, [16] describes a wavelet-base algorithm which
requires data continuously from the sensor nodes. To overcome these drawbacks, we have introduced an efficient
stream-based edge data processing and decision making
algorithm [9] which enables lightweight event-based communication.
Water Burst Localization. Over the last decade, there
are some pioneering techniques proposed for water burst
localization, such as wave propagation analysis [17], spectral
clustering, and multiple hypotheses testing [18] (see [19]
for a survey). Nonetheless, only a paucity of methods have
been proposed in the context of a water network structure
that explores graph topology. One excellent piece of work is
Misiunas et al. [20] who leveraged a search-based technique
to localize a burst point. Its main idea consists of two phases:
in the first phase, the search is performed globally over
all nodes in the network; in the second phase, if the burst
is inferred to have occurred along the pipe, extra nodes
are placed along each of the pipes and the global search
is repeated. However, both steps of this method require
that a global search over all sensor locations is performed.
Therefore, its computation is expensive and will have scale
issues in a water network with a high density of nodes.
Recently, Srirangarajan et al. [16] utilizes wave-based
multiscale analysis of pressure signals to detect burst transients. To localize burst events, they also exploited the Dijkstra’s algorithm for calculating the shortest distance between
every two sensor locations. Nevertheless, we observe that,
when a burst occurs, its wave may travel in all the possible
directions of the paths (rather than down only one path in one
direction with the shortest distance) from the burst location
to sensor points. Thus, to accurately position burst events, it
is not appropriate to depend only on the shortest travel time
between two sensor locations.
We have some prior work on localisation using graph
theory [21], [22], [23] but with pressure data only. Again,
not only have we reapplied this work to use vibration data,
which has some subtle differences, but we have integrated
the end-to-end localization systems for the first time and
successfully. That is, the edge anomaly detection and localization elements of the systems which produce a timely
localization result and reduce the communication by 99%
compare to the tradition periodic communication. Further,
this is the first use of the combination of manual and
automatic localization feedback information to tune the endto-end system parameters to maximize its performance in a
low-cost way.
VIII. C ONCLUSIONS
This paper presents a burst detection and localization
scheme that combines lightweight compression and anomaly
detection with graph topology analytics for water distribution networks. We show that our approach not only
significantly reduces the amount of communications between
sensor devices and the back end servers, but also can effectively localize water burst events by using the difference in
the arrival times of the vibration variations detected at sensor
locations. Our results can save up to 90% communications
compared with traditional periodical reporting situations.
Further our localisation can find the position of the anomaly
for our particular scenario within 0.5m error. This data
driven approach is significantly better than many hydraulic
modelling approaches that at best identify a leak to the
length of a given pipe which can be 10s of metres [24].
In this paper we show that early transient or event detection can run on low resourced sensor nodes meaning that
local control functions can occur with minimal latency and
this paves the way for distributed control for next generation
water networks. One can imagine that event time stamps are
sent to the back end to be localized and this information
fed into a control decision process (such as model driven
control) where the pipe network would be reconfigured
using remotely controlled valves to save both water and
customer demand issues. Such networks ultimately mean
a reduction of economic water scarcity due to poor water
network operation and at the same time make use of scarce
water resources.
ACKNOWLEDGMENT
The algorithmic work presented here forms part of the
Big Data Technology for Smart Water Nets research project
funded by NEC Corporation, Japan and EU FP7 WISDOM:
Water analytics and Intelligent Sensing for Demand Optimised Management project, FP7-ICT-2013-11 GA 619795.
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